The FCC requires that any station using more than 50W on VHF do a MPE evaluation, but handheld and mobile stations are usually exempt from doing these due to their low duty and push to talk nature. If you run >50W VHF at home you should consider RF exposure in case someone ever asks. I should also note that even if there is an exemption from the analysis, that does not mean you are exempt from the exposure rules regardless of your power. It's possible that even with 5W through a lot of gain to create a sizable local power density somewhere that just as harmful as 100W through a low gain antenna.
OTOH, there is a reason that 50W was deemed concerning and so there is nothing wrong with considering it in a mobile station.
Don't forget that the whip is not the only part of your station that can radiate RF. The ground might, the feedline certainly can and even the radio can generate a field. It's not a good idea to operate a VHF or UHF radio with the enclosure open, for the same reason it's not going to end well to run your microwave oven with the door open. These sources will generally be lower intensity than the antenna itself, but not always zero. For example, antenna couplers (e.g. tuners) can be a strong local source (particularly when NOT grounded!), but this is not really relevant to a VHF mobile. The biggest concern after the antenna itself would be the feedline, in particular bad connections or compromised coax. A bad solder joint at a PL-259/SO-239 or cut dielectric can be a decent radiator, it's essentially a mini antenna.
The IEEE recommendations show that the frequencies of most concern span 30-500MHz with the worst region being 100-300MHz. The 2m ham band falls right in the middle of that... At low frequencies there's less effect on humans and higher frequencies the power is attenuated quickly (short wavelength) so it does not take much distance to lower exposure. The VHF range starts to negatively affect humans but can have significant power density within large physical regions due to a longer wavelength.
The best way to know is to measure the field strength, but this is not always practical and so most hams do this analytically.
For 110W at 146MHz through a modest gain of 3.8dBi (e.g. 3.8dBi - 2.2dB = 1.6dBd, a 1/2 w.l. gain antenna) at 5 feet gives a predicted exposure of about 2.3mW/cm^2. The FCC allowable exposure for VHF is 1 mW/cm^2 for controlled and 0.2mW/cm^2 for uncontrolled. This would be considered non-complying exposure for all cases. If you go back and run the numbers at 10 feet, the level drops to 0.6mW/cm^2, which is acceptable for controlled exposure but still not allowable for uncontrolled. Ultimately you'll find that 17 feet is the minimum distance for uncontrolled exposure at 110W for VHF. For comparison, at 50W, these levels are achieved at about 5 feet and 12 feet. Something to think about if someone was putting up an antenna at home, try to keep 12' clear around it.
The difference between controlled and uncontrolled is determined if exposure time can be controlled, which for your station means that you have the ability to not transmit when someone is with the critical range. For amateur applications controlled would be your truck, house and yard, uncontrolled is areas beyond your control. Like your neighbor who doesn't know when you're transmitting and so could walk into and stand in a high exposure area for an unknown length of time. It's about heating on a human body, which is combination of power and time.
I would not be too concerned @110W under the roof if the antenna is right in the middle, but I would be mindful of anyone within a few feet. Remember that glass is not a great shield. Incidentally, this is another reason middle of the roof antennas are preferred for VHF, you have a good shield through a concerning range.